solving the sex ratio scandal in melittobia wasps · 2020. 11. 16. · produce less female-biased...

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Solving the sex ratio scandal in Melittobia wasps 6

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Jun Abe1, Ryosuke Iritani2, Koji Tsuchida3, Yoshitaka Kamimura4, and Stuart A. West5 8

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1Faculty of Liberal Arts, Meijigakuin University, Yokohama, Kanagawa 244-8539, Japan 10

2RIKEN Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS), Wako, Saitama 11

351-0198, Japan 12

3Faculty of Applied Biological Sciences, Gifu University, Gifu 501–1193, Japan 13

4Department of Biology, Keio University, Yokohama, Kanagawa 223-8521, Japan. 14

5Department of Zoology, Oxford University, Oxford, OX1 3PS, United Kingdom 15

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Correspondence and requests for materials should be addressed J. A. ([email protected]) 17

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Abstract 19

The scandalous sex ratio behaviour of Melittobia wasps has long posed one of the greatest problems 20

for the field of sex allocation. In contrast to the predictions of theory, and the behaviour of 21

numerous other organisms, laboratory experiments have found that Melittobia females do not 22

produce less female-biased offspring sex ratios when more females lay eggs on a patch. We resolve 23

this scandal, by showing that, in nature, females of M. australica have sophisticated sex ratio 24

behaviour, where their strategy also depends upon whether they have dispersed from the patch 25

where they emerged. When females have not dispersed, they will be laying eggs with close relatives, 26

which keeps local mate competition high, even with multiple females, and so they are selected to 27

produce consistently female-biased sex ratios. Laboratory experiments mimic these conditions. In 28

contrast, when females disperse, they will be interacting with non-relatives, and so they adjust their 29

sex ratio depending upon the number of females laying eggs. Consequently, females appear to use 30

dispersal status as an indirect cue of relatedness, and whether they should adjust their sex ratio in 31

response to the number of females laying eggs on the patch. 32

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Introduction 34

Sex allocation has produced many of the greatest success stories in the fields of behavioural and 35

evolutionary ecology1–4. Time and time again, relatively simple theory has explained variation in 36

how individuals allocate resources to male and female reproduction. Hamilton’s local mate 37

competition (LMC) theory predicts that when n diploid females lay eggs on a patch, and the 38

offspring mate before the females disperse, that the evolutionary stable proportion of male offspring 39

(sex ratio) is (n-1)/2n 5 (Fig. 1). A female-biased sex ratio is favoured to reduce competition 40

between sons (brothers) for mates, and to provide more mates (daughters) for those sons6–8. 41

Consistent with this prediction, females of > 40 species produce female-biased sex ratios, and 42

reduce this female bias when multiple females lay eggs on the same patch9 (higher n; Fig. 1). The fit 43



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of data to theory is so good that the sex ratio under LMC has been exploited as a ‘model trait’ to 44

study the factors that can constrain ‘perfect adaptation’ 4,10–13. 45

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Figure 1 | Local mate competition (LMC). The sex ratio (proportion of sons) is plotted versus the 47

number of females laying eggs on a patch. The right green dashed line shows the LMC theory 48

prediction for haplo-diploid species5,38. A more female-biased sex ratio is favoured in 49

haplo-diploids7,31. Females of many species adjust their offspring sex ratio as predicted by theory, 50

as observed in the parasitoid Nasonia vitripennis75 (green diamonds). In contrast, the females of 51

several Melittobia species, such as M. australica, continue to produce extremely female-biased sex 52

ratios, irrespective of the number of females laying eggs on a patch14 (blue squares). 53

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In stark contrast, the sex ratio behaviour of Melittobia wasps has long been seen as one of the 55

greatest problems for the field of sex allocation3,4,14–21. The life cycle of Melittobia wasps matches 56

the assumptions of Hamilton’s local mate competition theory5,14,19,21. Females lay eggs in the larvae 57

or pupae of solitary wasps and bees, and then after emergence, female offspring mate with the 58

short-winged males, who do not disperse. However, laboratory experiments on four Melittobia 59

species have found that females lay extremely female-biased sex ratios (1-5% males), and that these 60

extremely female-biased sex ratios change little with increasing number of females laying eggs on a 61



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patch14,17–20,22 (higher n; Fig. 1). A number of hypotheses to explain this lack of sex ratio adjustment 62

have been investigated and rejected, including sex ratio distorters, sex differential mortality, 63

asymmetrical male competition, and reciprocal cooperation14,16–18,20,22–26. 64

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We tested whether Melittobia’s unusual sex ratio behaviour can be explained by females being 66

related to the other females laying eggs on the same patch. After mating, some females disperse to 67

find new patches, while some may stay at the natal patch to lay eggs on previously unexploited 68

hosts (Fig. 2). If females do not disperse then they can be related to the other females laying eggs on 69

the same host27–30. If females laying eggs on a host are related, then this increases the extent to 70

which relatives are competing for mates, and so can favour an even more female-biased sex 71

ratio28,31–34. Although most parasitoid species appear unable to directly assess relatedness, dispersal 72

behaviour could provide an indirect cue of whether females are with close relatives35–37. 73

Consequently, we predict that when females do not disperse, and so are more likely to be with 74

closer relatives, they should maintain extremely female-biased sex ratios, even when multiple 75

females lay eggs on a patch28,34. 76

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Figure 2 | Host nest and dispersal manners of Melittobia. (a) Photograph of the prepupae of the 78

leaf-cutter bee Chalicodoma sculpturalis nested in a bamboo cane, and (b) diagram showing two 79

ways that Melittobia females find new hosts. The mothers of C. sculpturalis build nursing nests 80



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with pine resin consisting of individual cells, in which their offspring develop. If Melittobia wasps 81

parasitize a host in a cell, female offspring that mate with males inside the cell find a different host 82

on the same patch (bamboo cane) or disperse by flying to other patches. 83

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We tested this prediction in a natural population of a Melittobia species found in Japan, M. 85

australica. We examined how the sex ratio produced by females varies with the number of females 86

laying eggs on a patch, and whether or not they have dispersed before laying eggs. To match our 87

data to the predictions of theory, we developed a mathematical model tailored to the unique 88

population structure of Melittobia, where dispersal can be a cue of relatedness. We then conducted a 89

laboratory experiment to test whether Melittobia females are able to directly access the relatedness 90

to other females and adjust their sex ratio behaviour accordingly. Our results suggest that females 91

are adjusting their sex ratio in response to both the number of females laying eggs on a patch, and 92

their relatedness to the other females. But, relatedness is assessed indirectly, by whether or not they 93

have dispersed. Consequently, what appeared scandalous, instead reflects a more refined sex ratio 94

strategy. 95

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Results 97

Population structure and relatedness 98

To obtain the natural broods of Melittobia, we placed bamboo traps in the wild (Fig. 2). A total of 99

4890 host wasps and bees developed in these bamboo traps, with an average of 4.7 ± 2.9 (SD) hosts 100

per bamboo cane (Supplementary Table 2-1). Of these hosts, 0.94% were parasitised by M. 101

australica, and we obtained data from 29 M. australica broods in which all of the emerging 102

offspring were obtained (Supplementary Table 2-4). We assessed whether the mothers that had laid 103

these broods were from the same host patch (non-dispersers) or had dispersed from a different host 104

patch (dispersers), by examining other parasitised hosts on the same patch (bamboo trap). If there 105

were other parasitised hosts, we also confirmed whether they were dispersers form other patches by 106



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genotyping microsatellite DNA markers27. Overall, we found that 8 broods were laid by 107

non-dispersering females (5 – 36 mothers), 19 broods were laid by disperseing females (1 – 5 108

mothers), and 2 broods were laid by mixture of non-dispersers and dispersers (6 mothers). 109

110

In nature, we found that 55.2% (16/29) of broods were produced by more than one female. The 111

number of females producing a brood varied from 1 – 36, with an arithmetic mean of 6.7 and a 112

harmonic mean of 1.7 (Supplementary Table 2-2d). Broods where multiple females lay eggs are 113

therefore relatively common. Consequently, the lack of sex ratio adjustment, when multiple females 114

lay eggs on patch, cannot be explained by multiple female broods not occurring or being extremely 115

rare in nature10. In the two mixed broods, produced by non-dispersers and dispersers, single 116

dispersers produced all-male clutches, and other females were non-dispersers producing clutches 117

containing both sexes. We carried out analyses below discarding the two all-male clutches, because 118

we were interested in the sex allocation behaviour of mothers producing both sexes. However, we 119

found the same qualitative results irrespective of whether we removed the two broods laid by a 120

mixture of dispersers and non-dispersers (Supplementary Information 1). 121

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Our analysis of relatedness estimated by16 polymorphic microsatellite loci suggests that dispersing 123

females laying eggs on the same patch are unrelated, but that non-dispersing females laying eggs on 124

the same patch are highly related (Supplementary Information 1). As the number of females laying 125

eggs increased, the relatedness between females developing in a brood decreased when the brood 126

was produced by dispersing females, but not when the brood was produced by non-dispersing 127

females (Fig. 3a; dispersers: 21 = 10.15, P = 0.001; non-dispersers: 2

1 = 0.93, P = 0.33; interaction 128

between dispersal status and number of females laying eggs: 21 = 12.34, P < 0.01). The pattern of 129

relatedness for dispersers closely resembled that expected if unrelated females had produced the 130

broods, while the pattern for non-dispersers was clearly different from this expectation (Fig. 3a). 131



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The relatedness between the female offspring of non-dispersers remained high regardless of the 132

number of females laying eggs, suggesting that when multiple non-dispersing females laid eggs on 133

the same patch, they were inbred sisters. This was confirmed by our parentage analysis, which 134

suggests that when multiple non-dispersers contributed to a brood, they were offspring of a single 135

female or very closely related females. 136

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Figure 3 | Sex ratios and relatedness in nature. The relationship between the number of females 138

laying eggs on a patch and (a) the average relatedness between female offspring on a patch; (b) the 139

offspring sex ratio (proportion males). The dashed black line in (a) shows the expected relatedness 140

assuming that the mothers of the female offspring are not genetically related, (1 + 3f)/(2n(1 + f)), 141

where n is the number of mothers, and f is the inbreeding coefficient estimated as f = 0.631 from the 142



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microsatellite data. The solid red and blue lines in (b) represent the fitted lines of the generalized 143

linear mixed models assuming binomial distribution for dispersing and non-dispersing females, 144

respectively. The x-axes are logarithmic. When females disperse (red circles), an increasing number 145

of females laying eggs on a patch leads to a decrease in relatedness between female offspring (a) 146

and an increase in the offspring sex ratio (b). In contrast, when females do not disperse, neither the 147

relatedness between female offspring (a) nor the offspring sex ratio (b) significantly varies with the 148

number of females laying eggs on a patch. 149

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Sex ratios 151

There was a clear difference in the sex ratios (proportion of sons) produced by dispersing females 152

compared with non-dispersing females. As the number of females laying eggs on a patch increased, 153

dispersers produced less female-biased sex ratios, but non-dispersers did not (Fig. 3b; dispersers: 154

21 = 14.62, P < 0.001; non-dispersers: 2

1 = 0.56, P = 0.46; interaction between dispersal status 155

and number of females laying eggs: 21 = 18.69, P < 0.001). Consequently, while non-dispersers 156

always produced approximately 2% males, dispersers produced from 3 to 16% males, as the number 157

of females laying eggs increased. 158

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The pattern in non-dispersers is consistent with laboratory experiments. In laboratory experiments, 160

females were not given a chance to disperse, and as the number of females laying eggs was 161

increased from 1 – 16, there was only a very small increase in offspring sex ratio, from 1 – 2% 162

males14 (Fig. 1). In contrast, the increasing sex ratios observed in broods produced by dispersers is 163

consistent with the pattern predicted by Hamilton’s original LMC model5,38. The fit to Hamilton’s 164

theory is qualitative, not quantitative, as the observed sex ratios were more female biased. 165

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As also predicted by LMC theory, we found that when individual dispersing females produced more 167

of the offspring on a patch, they produced more female-biased offspring sex ratios39–41. The 168

offspring sex ratios produced by a dispersing female was significantly negatively correlated with 169



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the proportion of the brood that she produced (Fig. 4; 21 = 9.99, P = 0.002). This pattern is 170

predicted by theory, because when a female lays a greater proportion of the offspring on a patch, her 171

sons are more likely to be competing for mates with their brothers, and more likely to be mating 172

with their sisters. Consequently, when females produce a greater proportion of offspring on the 173

patch, their offspring will encounter greater LMC, and so more female-biased sex ratios are 174

favoured39–41. Analogous sex ratio adjustment in response to fecundity has been observed in a range 175

of species, including wasps, aphids, and cestodes39,42–45. 176

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Figure 4 | Sex ratios in response to relative brood size. Sex ratios produced by dispersing females 178

laying eggs with other dispersers decrease with an increasing proportion of focal female brood size 179

(focal female brood size divided by the total brood size produced), as expected in theory39–41. The 180

solid red line represents the fitted line of the generalized linear mixed model assuming binomial 181

distribution. 182

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Sex ratio and relatedness 184

Hamilton’s LMC theory can be rewritten to give the predicted sex ratio in terms of the relatedness 185

between the offspring on a patch, rather than the number of females laying eggs on a patch2,46. This 186



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is useful for examining Melittobia sex ratios, because it can apply to cases where relatedness 187

between offspring is influenced by multiple factors, including relatedness between mothers, and not 188

just the number of mothers2. 189

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We extended existing theory to examine the scenario where a fraction of females does not disperse, 191

and instead remain to lay eggs with related females28 (Supplementary Information 3). We assumed 192

the standard LMC scenario that n females lay eggs per patch, and that all mating occurs between the 193

offspring laid in a patch. However, we also assumed that patches survive into the next generation 194

with a probability 1 – e. If the patch survives, a fraction of female offspring become non-dispersers 195

remaining on the natal patch to reproduce, and others become dispersers. In contrast, with a 196

probability e the patch does not survive (goes extinct), and all female offspring become dispersers. 197

In the next generation, extinct patches were replaced with new patches, where dispersed females 198

from other patches can reproduce. 199

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Our model predicts: (1) as relatedness between offspring increases, a more female-biased sex ratio 201

is favoured; and (2) this predicted negative relationship is almost identical for dispersing and 202

non-dispersing females (Fig. 5a and Supplementary Fig. 3-2). The relationship is almost identical 203

because it is the increased relatedness between offspring on a patch that leads to competition and 204

mating between relatives, and hence favours biased sex ratios2. Increased relatedness can come 205

from either one or a small number of females laying eggs on a patch, or multiple related females 206

laying eggs. For a given number of females laying eggs on a patch, non-dispersing females will be 207

favoured to produce a more biased sex ratio (Supplementary Fig. 3-1), but this can also be 208

accounted for by the extent to which their offspring will be more related (Fig. 5b). Non-dispersing 209

females produce offspring that are more related, and so a more female-biased sex ratio is favoured 210

(Fig. 5a). For example, if five non-dispersing females lay eggs on a patch, then the relatedness 211



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between female offspring and offspring sex ratio are both predicted to be almost the same as those 212

for three dispersing females (Fig. 5b). 213

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Figure 5 | Sex ratios and relatedness. The predicted (a & b) and observed (c) relationship between 215

the offspring sex ratio, and the relatedness between female offspring on a patch. Our model predicts 216

that the evolutionarily stable (ES) sex ratio is negatively correlated with the relatedness between 217

female offspring (a & b; assuming haplo-diploid genetics, and e = 0.66, which is assigned from the 218

proportion of broods by dispersed females in the field). (a) The predicted relationships are almost 219

identical for dispersed females (red line) and non-dispersed females (blue line), which are also 220

equivalent to the prediction of Hamilton’s original local mate competition (LMC) model2 (green 221

dashed line). (b) The predicted sex ratio is shown when a given number of dispersing females (nE; 222

open red circle) or non-dispersing females (nN; open blue triangle) lay eggs on a patch. When more 223

than one (n > 1) female lays eggs on a patch, non-dispersing females are predicted to exhibit more 224

related females, and lower sex ratios. However, the overall relationship between the sex ratio and 225

relatedness is very similar for dispersing and non-dispersing females, because the prediction for 226

each number of dispersing females (nE) is approximately equivalent to that for a slightly lower 227

number of non-dispersing females (nN). For example, compare the predictions for nE = 3 and nN = 5. 228



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(c) Compared across natural broods, the offspring sex ratio was negatively correlated with the 229

relatedness between female offspring. While the sex ratios produced by dispersing females (solid 230

red circle) decrease with relatedness, the broods of non-dispersing females (solid blue triangles) 231

were all clumped at high relatedness/ low sex ratio. The solid black line in (c) represents the fitted 232

line of the generalized linear mixed model assuming binomial distribution for dispersing and 233

non-dispersing females. 234

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When we plotted the M. australica sex ratio data, for both dispersers and non-dispersers, there was 236

a clear negative relationship between the sex ratio and the relatedness between female offspring 237

(Fig. 5c; 21 = 25.86, P < 0.001). Relatedness between female offspring explained 72.2% of the 238

variance in the offspring sex ratio. This relationship is driven by relatively continuous variation 239

across the broods produced by dispersing females, and all the broods produced by non-dispersing 240

females being at one end of the continuum (Fig. 5c). When more dispersing females laid eggs on a 241

patch, this led the offspring being less related (Fig. 3a), and females produced a less female-biased 242

sex ratio (Fig. 3b). In contrast, in the broods produced by non-dispersers, neither the relatedness 243

between offspring or the offspring sex ratio varied significantly with the number of female laying 244

eggs on the patch (Fig. 3). Consequently, the broods of non-dispersers were all at the extreme end of 245

the relationship between offspring sex ratio and relatedness between female offspring (Fig. 5c). 246

247

These results show that the sex ratio behaviour of dispersing and non-dispersing females lays on the 248

same continuum, and explains why non-dispersers do not adjust their offspring sex ratios (Fig. 5c). 249

Non-dispersers are so related that the number of females laying eggs does not significantly 250

influence the relatedness between their offspring (Fig. 3a). Consequently, non-dispersers always 251

encounter extreme LMC, and are selected to produce consistently and highly female-biased 252

offspring sex ratios (Fig. 5a). 253

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Can females recognize relatives? 255



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Females could be assessing relatedness by either directly recognizing kin, or indirectly, by using 256

whether or not they have dispersed as a cue of whether they are likely to be with non-relatives 257

(dispersering females) or relatives (non-dispersering females)34–37. We conducted a laboratory 258

experiment to test whether females directly recognize the relatedness of other females laying eggs 259

on the same host, and adjust their sex ratio accordingly. We examined the sex ratio behaviour of 260

females who were either: (a) laying eggs on a host alone; (b) laying eggs with a related female in 261

the same inbred strain; (c) laying eggs with an unrelated female from a different inbred strain. 262

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We found that there was no significant influence of relatedness between females on the offspring 264

sex ratio that they produced. The sex ratio produced by females ovipositing with another female did 265

not differ significantly, depending upon whether the other female was related or not (Fig. 6; 21 = 266

0.66, P = 0.42). As has been found previously14,16,17, the sex ratio produced when two females laid 267

eggs together was slightly higher than when a female was laying eggs alone (21 = 20.5, P < 0.001), 268

but this shift was negligible compared to the predictions of Hamilton’s LMC theory5. Consequently, 269

it appears that females cannot assess relatedness directly, consistent with previous work on 270

Melittobia species16,25. 271

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Figure 6 | Sex ratios in the laboratory experiment. The number of replicates was 24 for each 273

treatment. Error bars represent standard errors. Statistical values indicate the result of a pairwise 274

comparison after correcting for multiple comparisons. Females show slightly increased sex ratios 275

when they lay eggs with another female, as previously observed14,16,17. However, they do not adjust 276

their sex ratios in response to relatedness to the females. 277

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Discussion 280

We found theoretically, that when the offspring on a patch will be more closely related, females 281

should produce more female-biased offspring sex ratios2 (Fig. 5a). In our model, the relatedness 282

between offspring is determined by both how many females laid eggs on a patch, and whether those 283

females (mothers) were had dispersed. Furthermore, we found that the predicted relationship 284

between sex ratio and relatedness is relatively invariant to whether variation in relatedness is caused 285

by the number of females laying eggs on a patch, or their dispersal status. Frank (1998) has 286

previously shown that one way of thinking about and analysing LMC, is that it is the relatedness 287

between offspring that determines the extent to which relatives are competing for mates, and mating 288

siblings, and hence the extent of LMC2. Our results support Frank (1998)2, showing that his 289



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prediction is very little altered when allowing for variable dispersal strategies. Overall, the 290

relatedness between female offspring was able to explain an impressive 72% of the variation in the 291

sex ratio data, which is far higher than the average of 28% for studies on LMC9. 292

293

We found that, in nature, M. australica females adjust their offspring sex ratio in the direction 294

predicted by our theoretical model (Fig. 5c). Females appear to do this by adjusting their offspring 295

sex ratio in response to two factors, the number of females laying eggs on a patch, and whether they 296

have dispersed (Fig. 3b). The influence of the number of females laying eggs has previously been 297

demonstrated in numerous species4. The more females lay eggs on a patch, the less related offspring 298

will be2,5,38. In contrast, the influence of dispersal status is relatively novel. Previous work on the 299

thrip Hoplothrips pedicularius suggests that non-dispersing females lay more female-biased sex 300

ratios, but it is not known if the offspring sex ratio is also adjusted in response to the number of 301

females laying eggs28. What is special about the pattern in M. australica is that females appear to 302

adjust their response to other females, depending upon whether they have dispersed or not – only 303

dispersed females lay less female-biased sex ratios when more females are laying eggs on a patch 304

(Fig. 3b). Consequently, M. australica females appear to use a relatively sophisticated strategy to 305

adjust their offspring sex ratios in response to the extent of LMC, as measured by the relatedness 306

between the offspring that will develop on that patch (Fig. 5). 307

308

M. australica females appear to assess their relatedness to other females indirectly, by their 309

dispersal status, rather than directly, by genetic cues. The optimal sex ratio depends upon 310

relatedness to other females laying eggs on the same patch, and so females will be selected to assess 311

relatedness. Our laboratory experiment suggests that females cannot assess relatedness directly (Fig. 312

6). The direct assessment of kin via genetic cues appears to be rare in parasitoids, with most studies 313

finding that females do not use genetic cues to assess relatedness to other females16,25,35–37,47. An 314



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exception is provided by the bethylid Goniozus nephantidis, where females appear to be able to 315

assess relatedness directly, and adjust their offspring sex ratio accordingly34,36. A possible reason for 316

the rarity of direct genetic kin recognition is that it is not evolutionarily stable, because selection 317

will favour more common markers, and hence eliminate the genetic variability required for kin 318

recognition48–50. In contrast, dispersal status appears to be an excellent indirect (environmental) cue 319

of relatedness28–30 – when females do not disperse, they are closely related to the other females 320

laying eggs on a patch, leading to their offspring being highly related (Fig. 3a). 321

322

While the pattern of sex ratio adjustment in M. australica is in the direction predicted by theory, the 323

fit to theory is qualitative not quantitative. The offspring sex ratios are more female biased than 324

predicted by theory (Fig. 5). One possible explanation for that is a cooperative interaction between 325

related females6,51–53. In Melittobia, females favor ovipositing on hosts parasitized by other females 326

rather than intact hosts (J. A. unpublished data). In addition, a larger number of Melittobia females 327

are likely to be advantageous to cooperatively make tunnels in host nests, and to fight against mite 328

species that lives symbiotically with host species54,55. Cooperative interactions have previously been 329

suggested to favour an increased proportion of female offspring in a range of organisms, including 330

other parasitoids, bees, beetles, and birds37,51,56–60. A complication here is that although limited 331

dispersal increases relatedness between encountering individuals, it can also increase competition 332

between the related individuals, and so reduce selection for female-biased sex ratios32,33,46,53,61. 333

However, in the case of Melittobia species, overlapping generations, inelasticity, dispersing with 334

relatives, and open sites could negate this increased competition33,62–65 (Supplementary Information 335

3) 336

337

To conclude, our results provide an explanation for the Melittobia sex ratio scandal. Laboratory 338

experiments on four Melittobia species have found that females produce lay extremely 339



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female-biased sex ratios (1 – 5% males), that change little with increasing number of females laying 340

eggs on a patch14,18–20,22 (Fig. 1). In laboratory experiments, females were not able to disperse, and 341

so they were likely to have behaved as non-dispersers, who would normally be on a patch with 342

close relatives. We found that, in natural conditions, non-dispersers behave as if other females are 343

close relatives, and show little response to the number of females laying eggs on the same patch 344

(Fig. 3b). So rather than being scandalous, the sex ratio behavior of Melittobia appears to reflect a 345

refined strategy, that also takes account of indirect cues of relatedness. 346

347

Methods 348

Parasitoid wasps 349

Melittobia australica (Hymenoptera: Eulophidae) is a gregarious parasitoid wasp that mainly 350

parasitizes prepupae of various solitary wasp and bee species nesting above ground. The host 351

species build nests containing brood cells, in which offspring develop separately while eating food 352

provided by their mothers. Several generations (5 or more on the main island of Japan) appear per 353

year in Melittobia species, while most of the host species are mainly univoltine. Multiple 354

generations of Melittobia may occur in a single host patch. Therefore, females laying eggs in 355

Melittobia could be derived from other broods in the same host patch or disperse from other patches 356

(Fig. 2). Once a female finds a host, she continues to lay eggs on the surface of the host, and is 357

potentially able to produce several hundred eggs on a single host as long as the host resources are 358

sufficient. Similar to other hymenopteran species, Melittobia exhibits a haplo-diploid sex 359

determination, in which male and female individuals develop from unfertilized and fertilized eggs, 360

respectively. Hatched larvae develop by sucking host haemolymph from the outside, and offspring 361

sequentially emerge from previously laid eggs. The adults of males are brachypterous, and do not 362

disperse from their natal host cells, in which they mate with females that develop on the same 363

host21. 364



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365

Field sampling 366

To collect the Melittobia broods from the field, we used bamboo traps, in which the host species 367

build nests to develop their offspring. We set up 7 – 32 bamboo traps at the end of July or the 368

beginning of August from 2011 – 2019 within an area with a 2 km radius in and around the campus 369

of Kanagawa University in Hiratsuka, Kanagawa, Japan (Supplementary Table 2-1). The traps were 370

horizontally fixed to the trunks or branches of trees at approximately 1.5 m above the ground. Each 371

bamboo trap consisted of a bundle of 20 dried bamboo canes. Each cane (200 – 300 mm long and 372

10 – 15 mm internal diameter) was closed with a nodal septum at one end and open at the other end. 373

The traps were collected between December and the following March, when the individuals of the 374

host wasps and bees in the cells were undergoing diapause at the prepupal stage. The traps were 375

brought back to the laboratory, where all of the canes were opened to inspect the interior. Along 376

with the traps that were set up in summer as described above, we conducted field sampling in the 377

spring of 2015, 2017, and 2018. Bamboo canes containing nests with host prepupae that were 378

collected in winter and kept in a refrigerator were exposed in the field for 1 – 2 months. 379

380

In the laboratory, all individuals of the solitary wasps and bees and their kleptoparasites and 381

parasitoids in the bamboo canes were counted and identified at the species level according to the 382

morphology of the juveniles and the construction of the nests (Supplementary Table 2-2). If they 383

were parasitized by Melittobia species, we recorded the host and Melittobia species (Supplementary 384

Table 2-3). The adults and the dead bodies of Melittobia females in the host cells or cocoons could 385

be regarded as mothers that laid eggs in the broods, if the next generation had not yet emerged. We 386

could distinguish female offspring from mothers based on the filled abdomen of emerged females. 387

We collected the mothers, and preserved them in 99.5% ethanol. After removing the mothers, the 388

parasitized hosts were individually incubated at 25°C until the offspring emerged. Emerged 389



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individuals were counted, sexed, and preserved in 99.5% ethanol. 390

391

Molecular analysis 392

For the analysis of sex ratios and molecular genetics, we only adopted the broods of M. australica 393

among the two collected species (Supplementary Table 2-4), because this species was dominant in 394

the present sampling area, and most of the applied microsatellite markers indicated below were only 395

valid for this species27. We also only included broods in which all the individuals of the offspring 396

generation had not yet started to emerge. The existence of emerged offspring in the host cells may 397

indicate that some females had already dispersed. Finally, we excluded clutches in which 16 or 398

fewer individuals emerged, or the majority of juveniles were destroyed by an accidental event such 399

as host haemolymph flooding. For genotyping, we analysed 16 female offspring that were randomly 400

selected from all emerged females in each clutch. For mothers and male offspring, we genotyped all 401

individuals if the number of individuals was less than 16; otherwise, 16 randomly selected 402

individuals were analysed. 403

404

We used the boiling method for DNA isolation (Abe et al. 2009). DNA was isolated from the whole 405

body for male individuals, or from the head and thorax for female individuals to prevent the 406

contamination of spermatozoa from their mates. For the genomic analysis, we selected 16 407

microsatellite markers out of 19 markers27 to avoid the use of markers that might show genetic 408

linkage with other loci. The detailed polymerase chain reaction methods are described elsewhere27. 409

The microsatellite genotypes of each individual were identified from the amplified DNA fragments 410

through fragment analysis with an ABI 3130 capillary sequencer (Life Technologies, Carlsbad, CA, 411

USA) and Peak Scanner software version 1.0 (Life Technologies, Carlsbad, CA, USA). Based on 412

the genotyping data, the average relatedness between the individuals on the broods and inbreeding 413

coefficient were calculated using the software Relatedness version 4.2b66. The broods were equally 414



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weighted in all analyses. We estimated the relatedness between the female offspring in a brood as a 415

representative metric of patch relatedness, because we could obtain a sufficient number of female 416

offspring from all the patches. 417

418

Although adult females that were captured in the broods of developing offspring could be regarded 419

as females laying eggs, all of the females might not necessarily contribute the broods, and other 420

females might depart before collection. We conducted a parentage analysis to reconstruct the 421

genotypes of females laying eggs (mothers) from the genotypic data of the offspring following the 422

Mendelian rules under haplo-diploidy (Supplementary Table 2-6). We first assigned the minimum 423

number of captured adult females as the candidate mothers. If we could not identify the candidates 424

from the captured females, we assumed that additional females produced offspring in the brood, and 425

rebuilt their genotypes. For assignment, we adopted the solution with the minimum number of 426

mothers producing broods. We also assumed that mothers mated with multiple but possibly minimal 427

numbers of males. Consequently, the genotypes of the mothers could be uniquely determined for 428

dispersers, and the number of mothers was strongly correlated with that of captured females 429

(Pearson’s correlation: r = 0.84, t = 6.51, df = 17, P < 0.001). However, we could not uniquely 430

determine the genotypes of mothers for non-dispersers, because of the high similarity of the 431

genotypes of the captured females. Then, we used the number of captured females as the number of 432

mothers for non-dispersers, although this may be an overestimation. 433

434

Laboratory experiment 435

A female was introduced into a plastic case (86 mm in diameter and 20 mm in height) (a) alone, (b) 436

with a related female from the same inbred strain, or (c) with an unrelated female from a different 437

strain, and allowed to lay eggs on a prepupa of Chalicodoma sculpturalis for 12 days. All the 438

females of the same strains were collected from a single prepula of C. sculpturalis that was 439



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parasitized by 8 females randomly chosen among the laboratory strains. The laboratory strains were 440

the Amami strain (AM) and the Shonan 1 or 2 strain (SN1 or SN2), which were initiated by 441

wild-caught wasps from single hosts collected from Amami Oshima Island in 2007 and from 442

Hiratsuka in 2017, respectively. Amami Oshima and Hiratsuka are located approsimately 1200 km 443

away, and are separated by sea. The Shonan 1 and 2 strains originated in the same population, but 444

were developed from individuals caught by different bamboo traps. The Amami and Shonan strains 445

were maintained in the laboratory for approximately 70 and 10 generations, respectively, during 446

which several dozen females from previous generations were allowed to lay eggs on prepupae of C. 447

sculpturalis to produce the subsequent generations. This procedure mimics the situation in which 448

non-dispersed females produce a new brood on another host in the same patch in the field. Before 449

the experiment, a female was allowed to mate with a male from the same strain in the manner 450

described elsewhere17. The emerged offspring were counted and sexed. In the treatment involving 451

two females from different strains, all male and 16 randomly collected female offspring were 452

genotyped for one of the microsatellite loci27, and the offspring sex ratios of the two ovipositing 453

females were estimated separately using the ratio of the genotyped individuals. In the treatment 454

involving females from the same strain, the two females were assumed to equally contribute to the 455

clutches. The experiment was conducted at a temperature of 25°C and a photoperiod of L16:D8 h. 456

457

Statistical analysis 458

We analysed all data using generalized linear mixed models implemented in statistical software R 459

version 3.6.1 67. The data on the number of females laying eggs or offspring, the sex ratio, the injury 460

frequency, and relatedness were fitted with Poisson, binomial, binomial, and beta distributions, 461

respectively. Because, multiple broods in the same bamboo canes were estimated to be produced by 462

females from the same hosts in some broods by non-dispersers, we added the bamboo cane to the 463

models as a random effect. In addition, we added the individual brood as a random effect for count 464



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data (the number of females laying eggs or offspring) or proportional data (sex ratio) to resolve the 465

problem of over-dispersion. We first ran full models including all fixed effects of interest and 466

random effects, and then simplified the models by removing non-significant terms ( > 0.05) from 467

the least significant ones to arrive at the minimum adequate models68. The statistical significance 468

was evaluated by using the likelihood ratio test comparing the change in deviance between the 469

models. In multiple comparisons, significance thresholds were adjusted using the false discovery 470

rate69. 471

472

Theoretical model 473

We assume a population consisting of infinite discrete patches, in which emerged male and female 474

offspring mate at random70 (Wright’s islands model of dispersal). We define the patch extinction 475

rate e as the probability that patches will go extinct, and be replaced by new patches. If the patches 476

go extinct (which occurs with a probability of e), all developed female offspring on the patches 477

disperse to other patches. In contrast, if a patch has survived (with a probability of 1 – e), female 478

offspring do not disperse with a probability of 1 – d, or otherwise disperse with a probability of d. 479

Non-dispersers remain on their natal patch, in which n randomly selected females reproduce in the 480

next generation. Dispersers from all the patches compete for reproduction on the newly created 481

patches, in which n randomly selected females reproduce. We use the subscript i to denote 482

dispersers (i = E) or non-dispersers (i = N). Let xi denote the sex ratio of a focal female, yi denote 483

the average sex ratio in the same patch as the focal female, and zi denote the average sex ratio in the 484

whole population. Then, the relative fitness of a daughter of the focal female 𝑤𝑖𝐅 and the relative 485

fitness of a son of the focal female 𝑤𝑖𝐌 may be written as follows: 486

𝑤𝑖𝐅 = (1 − 𝑥𝑖) [(1 − 𝑒)(1 − 𝑑)

𝑛

(1 − 𝑑)𝑛(1 − 𝑦𝑖)+{(1 − 𝑒)𝑑 + 𝑒}

𝑒𝑛

{(1 − 𝑒)𝑑 + 𝑒}𝑛(1 − 𝑧̅)] 487

= (1 − 𝑥𝑖) {(1 − 𝑒)1

1 − 𝑦𝑖+ 𝑒

1

1 − 𝑧̅}, (1) 488



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𝑤𝑖𝐌 = 𝑥𝑖

1 − 𝑦𝑖

𝑦𝑖[(1 − 𝑒)(1 − 𝑑)

𝑛

(1 − 𝑑)𝑛(1 − 𝑦𝑖)+{(1 − 𝑒)𝑑 + 𝑒}

𝑒𝑛

{(1 − 𝑒)𝑑 + 𝑒}𝑛(1 − 𝑧̅)] 489

= 𝑥𝑖

1 − 𝑦𝑖

𝑦𝑖{(1 − 𝑒)

1

1 − 𝑦𝑖+ 𝑒

1

1 − 𝑧̅}, (2) 490

respectively, where 𝑧̅ represents the metapopulation-wide average sex ratio: 491

𝑧̅ = 𝜋0𝑧E + ∑ 𝜋𝜏𝑧N+∞𝜏=1 (3) 492

and is the frequency of patches that were recolonized during generations. Note that the 493

parameter d is cancelled out as dispersers compete only with dispersers, while non-dispersers only 494

with non-dispersers. By applying the neighbour-modulated fitness approach to kin selection 495

methodology2,71–74, we find that an increased sex ratio is favoured by natural selection for dispersers, 496

if: 497

𝑒[𝑐𝐌(𝑟ES − 𝑟E

M) − (𝑐𝐌𝑟ES + 𝑐𝐅𝑟E

D)𝑧E](1 − 𝑧E) 498

+(1 − 𝑒)[𝑐𝐌(𝑟ES − 𝑟E

M) − {𝑐𝐌(𝑟ES − 𝑟E

M) + 𝑐𝐅(𝑟ED − 𝑟E

F)}𝑧E](1 − 𝑧̅) > 0, (4) 499

and for non-dispersers, if: 500

𝑒[𝑐𝐌(𝑟NS − 𝑟N

M) − (𝑐𝐌𝑟NS + 𝑐𝐅𝑟N

D)𝑧N](1 − 𝑧N) 501

+(1 − 𝑒)[𝑐𝐌(𝑟NS − 𝑟N

M) − {𝑐𝐌(𝑟NS − 𝑟N

M) + 𝑐𝐅(𝑟ND − 𝑟N

F)}𝑧N](1 − 𝑧̅) > 0, (5) 502

where cM and cF are the class reproductive values for females and males, respectively, 𝑟ES, 𝑟E

D, 𝑟EM, 503

and 𝑟EF are the kin selection coefficients of relatedness for a daughter, a son, a random male 504

offspring on the same patch, and a random female offspring on the same patch, respectively, from a 505

perspective of a disperser, and 𝑟NS, 𝑟N

D, 𝑟NM, and 𝑟N

F are the average kin selection coefficients of 506

relatedness for a daughter, a son, a random male offspring on the same patch, and a random female 507

offspring on the same patch, respectively, from a perspective of a non-disperser. Substituting the 508

terms of reproductive values and relatedness, we may derive the convergence stable sex ratios for 509

dispersers (𝑧E∗) and non-dispersers (𝑧N

∗ ). If we replace e with 1 − (1 − 𝑑)2, where d is female 510

dispersal rate after mating, we recover Gandner et al.’s (2009) results33. A full derivation is given in 511

Supplementary Information 3. 512



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513

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to J. A. 670

671

Author contributions 672

J. A., Y. K., and S. A. W. initiated, planned, and coordinated the project; J. A. collected and analysed 673

field, molecular, and laboratory data; R. I. and J. A. constructed the theoretical model; K. T. 674

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676

Competing interests 677

The authors declare no competing financial interests. 678



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Supplementary information 1 1

Solving the sex ratio scandal in Melittobia wasps 2

Jun Abe, Ryosuke Iritani, Koji Tsuchida, Yoshitaka Kamimura, and Stuart A. West 3

4

5

Field data 6

We obtained 46 broods of Melittobia australica with bamboo traps placed in the wild, and 11 7

broods by reexposing upparasitised hosts in the field (Supplementary Table 2-1, 2-2). All of the 8

emerging offspring were obtained with sufficient confidence from 29 of the collected broods, so we 9

analysed these broods (Supplementary Table 2-3). Our parentage analysis with the microsatellite 10

genotypic data indicated that all but two of the 29 broods were founded by either only dispersers or 11

only non-dispersers (Supplementary Table 2-3, S2-4). In the two other broods, non-dispersers 12

produced male and female offspring, while a single disperser added an all-male clutch. In both 13

broods, 5 non-dispersers were collected with developing offspring on the host, while the disperser 14

was not collected (Supplementary Table 2-4), suggesting that she had left the host before collection. 15

The single dispersers produced 75.0% (50.3/67) and 87.5% (66.5/76) male individuals, respectively, 16

in the broods. We were not certain whether the females producing all-male clutches were virgins, 17

although their behaviour is different from that of virgin females in the laboratory, in which they 18

produced only a few (maximally 9) male offspring before they mate with their own sons (Abe et al. 19

2010). 20

21

Genetic structure. To examine genetic differentiation depending on the behaviour of females 22

laying eggs, hierarchical population structure was analysed in microsatellite data using the R 23

package hierfstat (Goudet 2005). When we consider a structure, in which the entire population 24

(population) is divided into two groups of dispersers and non-dispersers (group), and each group is 25

divided by the genetic lineages of the females (lineage), the effect of group was not significant 26

(Fgroup/population = 0.011, P = 0.43), suggesting that there is no genetic differentiation between 27

non-dispersers and dispersers. When we instead divided the entire population into two groups of 28

all-male producers and the other females, the effect of group was not significant (Fgroup/population = 29

–0.020, P = 0.30), suggesting that there was no genetic differentiation between the females that 30

produced all-male clutches and those that produced clutches containing both sexes. 31

32

The number of females laying eggs. Over 10-fold more non-dispersers laid eggs on a single host 33

(mean ± SD = 16.6 ± 11.9) compared with dispersers (mean ± SD = 1.4 ± 1.1; Supplementary Table 34

2-3; 21 = 16.54, P < 0.001). The effect of host species on the number of females laying eggs per 35

brood was marginally non-significant (25 = 10.81, P = 0.055). 36

37

Brood size. Non-dispersers produced more offspring than dispersers in a single brood, although 38



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2

there were no significant effects of females laying eggs or host species (Supplementary Table 1-1a, 39

2-3). However, the number of females laying eggs was highly related to the dispersal status of the 40

females, as shown above. When we analysed the model after removing the dispersal status term, 41

offspring number significantly increased with the number of females, but host species was still 42

non-significant (Supplementary Table 1-1b). 43

44

Supplementary Table 1-1a. Analysis of total brood size (with dispersal status).

Removing two all-male clutches Removing two mixed broods

Minimal adequate model

Dispersal status 21 = 14.01 P < 0.001 2

1 = 13.83 P < 0.001

Non-significant terms deleted

Female number 21 = 2.57 P = 0.11 2

1 = 2.86 P = 0.091

Host species 25 = 1.67 P = 0.89 2

4 = 1.42 P = 0.84

45

Supplementary Table 1-1b. Analysis of total brood size (without dispersal status).



Female number 21 = 9.61 P = 0.002 2

1 = 13.52 P < 0.001


Host species 25 = 3.06 P = 0.69 2

4 = 2.13 P = 0.71

46

Relatedness. We adopted relatedness between female offspring in a brood to assess the kinship 47

between individuals on a patch, because we could obtain a sufficient number of female offspring in 48

all the broods analysed (Supplementary Table 2-3). Relatedness between female offspring showed a 49

significant interaction between the number of females laying eggs and the dispersal status of the 50

females (Fig. 3a), although brood size and host species were non-significant (Supplementary Table 51

1-2a). When we analysed the model for each dispersal status separately, relatedness significantly 52

decreased with an increasing female number in the broods of dispersers (Supplementary Table 1-2b), 53

but relatedness was independent of female number in the broods of non-dispersers (Supplementary 54

Table 1-2c). 55

56

57

58

59

60

61

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Supplementary Table 1-2a. Analysis of relatedness between female offspring in a brood (including both type

of females).



Female number NA NA

Dispersal status NA NA

Female number : Dispersal status 21 = 12.34 P < 0.001 2

1 = 11.97 P < 0.001


Brood size 21 = 2.67 P = 0.10 2

1 = 2.31 P = 0.13

Host species 25 = 5.47 P = 0.36 2

4 = 5.09 P = 0.28

63

Supplementary Table 1-2b. Analysis of relatedness between female offspring in a brood (only dispersers).



Female number 21 = 10.15 P = 0.001 2

1 = 10.15 P = 0.001

64

Supplementary Table 1-2c. Analysis of relatedness between female offspring in a brood (only non-dispersers).



Female number 21 = 0.93 P = 0.33 2

1 = 0.88 P = 0.35

65

Sex ratio. Sex ratios were clearly categorized into two groups depending on the dispersal status of 66

females (Fig. 3b): the interaction term between the number of females laying eggs and their 67

dispersal status was significant (21 = 18.95, P < 0.001), although host species and brood size were 68

not significant (Supplementary Table 3-1a). Separate model analysis for each dispersal status 69

showed that dispersers increased the sex ratio by increasing the number of females laying eggs 70

(Supplementary Table 3-1b), whereas non-dispersers did not (Supplementary Table 3-1c). When we 71

analysed sex ratios against relatedness between female sffspring incorporating the broods of both 72

dispersers and non-dispersers, a significant negative relationship between the sex ratio and 73

relatedness was found (Supplementary Table 1-4). 74

75

76

77

78

79

80

81



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4

Supplementary Table 1-3a. Analysis of sex ratio (both type of females).



Female number NA NA

Dispersal status NA NA

Female number : Dispersal status 21 = 18.69 P < 0.001 2

1 = 18.70 P < 0.001


Host species 25 = 8.40 P = 0.16 2

4 = 7.40 P = 0.12

Brood size 21 = 0.095 P = 0.76 2

1 = 1.60 P = 0.21

82

Supplementary Table 1-3b. Analysis of sex ratio (only dispersers).



Female number 21 = 14.62 P < 0.001 2

1 = 14.62 P < 0.001

83

Supplementary Table 1-3c. Analysis of sex ratio (only non-dispersers).



Female number 21 = 0.56 P = 0.46 2

1 = 0.015 P = 0.90

84

Supplementary Table 1-4. Analysis of sex ratio against relatedness between female offspring in a brood.



relatedness 21 = 25.86 P < 0.001 2

1 = 24.27 P < 0.001

85

86



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Laboratory data 87

Brood size. The number of offspring produced by a female was not influenced by the treatment 88

(Supplementary Fig. 1-1a; 22 = 0.70, P = 0.70) or strain (2

2 = 3.84, P = 0.15). 89

90

Sex ratio. Although the offspring sex ratio was significantly different depending on the treatment 91

(22 = 21.27, P < 0.001), this relied on the difference in foundress numbers (2

1 = 20.5, P < 0.001), 92

but the sex ratios produced by two related and unrelated females were not significantly different 93

(Fig. 5; 21 = 0.66, P = 0.42). The strain did not have a significant effect on the sex ratio 94

(Supplementary Fig. 1-2b; 22 = 1.50, P = 0.47). 95

96

Injury level. Fortuitously, we observed fighting between females in the experiment, which has 97

rarely been documented in Melittobia (Matthews & Deyrup 2007). Parts of the antennae and legs of 98

females were likely to be cut off by the opponent female during the 8 days after the introduction of 99

the females. However, the frequency of the injured females was not influenced by relatedness 100

(Supplementary Fig. 1-1c; 21 = 0.05, P = 0.82), although female pugnacity significantly varied 101

among the strains of females (21 = 18.32, P < 0.001). Ultimately, we found no evidence that 102

females adjust their behaviour depending on relatedness. Moreover, females could potentially 103

assessed relatedness indirectly on the basis of environmental cues, such as recognizing whether the 104

opponent females emerged from the same or different host. However, the present experiment, in 105

which all females of the same strain that were used were developed on the same host, suggested that 106

this possibility is not the case in the studied species. 107

108

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110

SN1 SN2 AM SN1 SN2 AM SN1 SN1 AM SN2 SN2 AM

No opponent

(a)

(b)

(c)

0.03

0.02

0.01

0

1

0.8

0.6

0.4

0.2

0

800

600

400

200

0

1 female 2 related females 2 unrelated females

Inju

ry f

requ

ency

of

opp

on

ent

fem

ale

Sex

rat

io

(pro

po

rtio

n o

f m

ales

) C

lutc

h s

ize

Figure S1-1. Clutch size (a), sex ratio (b), and injury frequency of opponent female (c) depending on treatment

regulating female number and their relatedness, and the strains of the females. Error bars represent standard errors (a,

b) and 95% binomial confidence intervals (c). The number of replicates was 8 for each strain in all the treatments.



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References 111

Abe, J., Innocent, T. M., Reece, S. E., & West, S. A. (2010) Virginity and the clutch size behaviour 112

of a parasitoid wasp where mothers mate their sons. Behavioral Ecology, 21.4, pp.730–738. 113

doi:10.1093/beheco/arq046 114

Matthews, R. W. & Deyrup, L. D. (2007) Female fighting and host competition among four 115

sympatric species of Melittobia (Hymenoptera: Eulophidae). The Great Lakes Entomologist, 40. 116

1, pp.52-68. Available at: https://scholar.valpo.edu/tgle/vol40/iss1/6 117



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Supplementary Information 3 for:

Solving the sex ratio scandalinMelittobiawasps

Jun Abe, Ryosuke Iritani, Koji Tsuchida, Yoshitaka Kamimura, and Stuart A WestNovember 12, 2020

Contents1 Model assumptions 1

2 Patch dynamics 1

3 Consanguinity 1

3.1. Diploidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3.2. Haplodiploidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4 Average and initial consanguinity coefficients 6

4.1. Diploidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.2. Haplodiploidy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Fitness subcomponents 9

6 Total fitness 11

7 Reproductive value 11

8 Selection gradient 11

9 Unconditional strategy 12

10 Dispersers’ strategy 13

11 Non-dispersers’ strategy 13

12 Evolutionary outcomes 13



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1 Model assumptions1

We use a spatially implicit model of dispersal (Wright’s islands model; Wright 1931), in which each2

patch may go extinct at a probability e. If patches go extinct, the same number of empty patches are3

recolonized in the next generation. Therefore, each patch is characterized by the age τ, where τ is the4

number of generations that have passed since a patch was recolonized.5

2 Patch dynamics6

Let πτ be the frequency of the patches aged τ. Under completely random extinction, the frequency7

of patch ages is updated by:8

πτ+1 = (1 − e)πτ , (S-1)

with9

π0 = e ×+∞∑τ=0

πτ︸︷︷︸random extinc

= e.(S-2)

Hence, the stationary distribution of the patches aged τ is given by:10

πτ = e(1 − e)τ ; (S-3)

that is, τ follows a geometric distribution.11

3 Consanguinity12

Under the assumptions that females andmalesmatewithin their natal patches and nnon-dispersing13

females reproduce in persistent patches, while n dispersing females from other patches reproduce in14

recolonized patches, consanguinity coefficients (the probability that randomly taken homologous15

genes of interest are identical by descent) may be derived for diploid and haplodiploid populations as16

below.17

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3.1. Diploidy18

The consanguinity coefficient fτ between a randommating pair on a patch aged τ is given by a well19

known recursion (Taylor 1988a,b; Frank 1998; Rousset 2004; Lehmann 2007; Gardner et al. 2009):20

fτ+1 =1n∙

12

(1 + fτ−1

2

)︸︷︷︸

=pIτ

+12fτ

+n − 1n

fτ , (S-4)

in which identical by decent (IBD) betweenmating partners occurs when (i) they share share the same21

mother 1 ∕ n, in which case the consanguinity is given by (i-a) the probability that both genes are from22

the same-sex parent 1/2 (i.e., both from the mother, or both from their father) times the consanguinity23

to self pIτ = (1 + fτ−1) ∕ 2 in the previous generation plus (i-b) the probability that their genes derive from24

opposite-sex parents 1/2 (i.e., one frommother and the other from father) times the consanguinity25

between the parents in the previous generation (fτ), or when (ii) they have different mothers (1 − 1 ∕ n),26

in which case the consanguinity is given by the probability that two distinct adults share the common27

ancestor in the previous generation fτ .28

The “initial” consanguinity (gifted by dispersers) reads:29

f0 =1n

+∞∑τ=0

(12pIτ +

12fτ

)πτ +

n − 1n

∙ 0, (S-5)

which is reasoned as follows: with a probability 1 ∕n, two female offspring share the dispersedmother, in30

which case their consanguinity is the metapopulation-wide average of (1 + 3fτ−1) ∕ 4. With a probability31

of 1 − 1 ∕ n, two female offspring have different, dispersed mothers, in which case consanguinity is null.32

Also we need to construct a recursion for pIτ , which for τ ≥ 1 reads:33

pIτ =

1 + fτ−12

, (S-6)

because with probability 1/2, the same homologous allele is sampled, in which case IBD is 1, and with34

probability 1/2, the other is sampled, in which case IBD is given by the consanguinity with her mating35

partner fτ−1. The initial condition for pI0 is given by:36

pI0 =

+∞∑τ=0

1 + fτ2

πτ (S-7)

From these, we get the consanguinity coefficient between a random adult female and her own sons37

or daughters (pSτ or p

Dτ , respectively) and that between a random adult female and a random offspring38

2



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born in the same patch (pMτ or p

Fτ , respectively) for τ ≥ 0:39

pSτ+1 = pD

τ+1 =12pIτ+1 +

12fτ ,

pMτ+1 = pF

τ+1 =1npSτ+1 +

n − 1n

fτ ,(S-8)

the first line of which reads as the probability that offspring’s allele derives frommother (1/2) times40

the probability that this allele is IBD with the mother (pIτ+1 = (1 + fτ)/2), plus the probability that the41

allele derives from father (1/2) times the probability that this allele is IBD with the mother (fτ). The42

second line is because, for a given allele sampled from a random adult female, an allele sampled from43

one of the offspring born in the same patch derives from the adult female (1 ∕ n; in which case the44

consanguinity is pSτ+1 = pD

τ+1) or another adult female (1 − 1 ∕ n; in which case the consanguinity is fτ).45

The initial conditions for τ = 0 (with Eqn (S-5)) are given by:46

f0 =+∞∑τ=0

pIτ + fτ2n

πτ

pS0 = pD

0 =

+∞∑τ=0

pIτ + fτ2

πτ ,

pM0 = pF

0 =1npS0 =

1npD0

(S-9)

where the first line follows because the consanguinity of a mother to one of her own offspring is the47

arithmetic mean (1/2) for herself (the former) and her mate (latter).48

3.2. Haplodiploidy49

Wedenote the consanguinity ofmating partners on the patch aged τ by fτ ; the average consanguinity50

of two female offspring sharing the same patch aged τ by ϕτ ; the average consanguinity between two51

male offspring sharing the same patch aged τ by μτ .52

The consanguinity between a pair of offspring male and offspring female on the same patch aged53

τ+1 is given by the probability that they share the samemother (1∕n) times the consanguinity of full sibs54

(with probability 1∕2, the offspring female derives her gene from her mother as does the offspring male,55

in which case the consanguinity is pIτ ; with probability 1 ∕2, the offspring female derives her gene from56

the father while the offspring male derives his gene from his mother, in which case the consanguinity57

is fτ) plus the probability that they do not share the same mother (1 − 1 ∕ n) times the probability that58

their mothers are both non-disperser (which is 1 since τ +1 ≥ 1) times the consanguinity of the parents59

by which their genes are transmitted (which isϕτ2+fτ2). That is:60

fτ+1 =1n∙

(12pIτ +

12fτ

)+n − 1n

∙

(ϕτ + fτ

2

)(S-10)

3



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(Taylor 1988a,b; Frank 1998; Rousset 2004; Lehmann 2007; Gardner et al. 2009).61

The average consanguinity of two female offspring sharing the same patch aged τ > 0, ϕτ , is given62

by the probability that they share the same mother (1 ∕ n) times the consanguinity of full sisters63

(pIτ ∕4 + fτ ∕2 + 1 ∕4) plus the probability that they do not share the same mother (1 − 1 ∕n) times the64

probability that their mothers are both non-dispersers (which is 1 since τ + 1 ≥ 1) (with probability65

1 ∕4 they both derived their genes from their mothers, in which case the consanguinity is ϕτ ; with66

probability 1 ∕2 they derived their genes from opposite-sex parents, in which the consanguinity is fτ ;67

with probability 1 ∕4 they both derived their genes from their fathers, in which case the consanguinity68

is μτ). That is,69

ϕτ+1 =1n∙

(14pIτ +

12fτ +

14

)+n − 1n

∙

(ϕτ + 2fτ + μτ

4

). (S-11)

The average consanguinity of two male offspring sharing the same patch (aged τ + 1 ≥ 1), μτ , is the70

probability that they share the same mother (1 ∕n) times the probability of full brothers pIτ plus the71

probability that they do not share the common mother 1 − 1 ∕ n times the probability that both of their72

mothers are non-disperser (which is 1 since τ + 1 ≥ 1) times the average consanguinity of two female73

offspring on the same patch ϕτ . That is:74

μτ+1 =1npIτ +

n − 1n

ϕτ . (S-12)

Finally, pIτ+1 (the consanguinity for herself) follows a recursion given by:75

pIτ+1 =

1 + fτ2

, (S-13)

as with probability 1/2, the same allele is sampled twice (in which case IBD is 1) and with probability76

1/2, two different homologous alleles are sampled (in which case IBD is given by the inbreeding77

coefficient in the previous generation, fτ).78

For a patch that is newly recolonized (i.e., aged τ = 0), kinship is possible for sibs (i.e., only by79

sharing the mother). The consanguinity between a pair of mating partners on the patch is given by the80

probability that they share the mother (1 ∕n) times the spatial average of the consanguinity of full sibs:81

f0 =1n∙

+∞∑τ=0

1 + 3fτ4

πτ . (S-14)

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Similarly,82

ϕ0 =1n∙

+∞∑τ=0

3 + 5fτ8

πτ ,

μ0 =1n∙

+∞∑τ=0

1 + fτ2

πτ ,

pI0 =

+∞∑τ=0

1 + fτ2

πτ .

(S-15)

(f0,ϕ0, μ0, pI0) gives the initial condition of the recursion. Solved recursively, (fτ ,ϕτ , μτ , pI

τ ) specifies the83

consanguinity between a mating pair, female offspring, and male offspring, respectively. From these,84

we get:85

pSτ = pI

τ ,

pMτ =

1npSτ +

n − 1n

ϕτ−1 ≡ μτ ,

pDτ =

pIτ + fτ−12

=1 + 3fτ−1

4,

pFτ =

1npDτ +

n − 1n

∙ϕτ−1 + fτ−1

2≡ fτ .

(S-16)

The initial condition for τ = 0 is given by:86

pS0 =

+∞∑τ=0

1 + fτ2

πτ ,

pM0 =

pS0

n,

pD0 =

+∞∑τ=0

1 + 3fτ4

πτ ,

pF0 =

pD0

n.

(S-17)

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4 Average and initial consanguinity coefficients87

4.1. Diploidy88

We consider the average values of fτ and pIτ over the distribution πτ :89

f :=+∞∑τ=0

fτπτ

pI :=

+∞∑τ=0

pIτπτ .

(S-18)

By multiplying πτ+1 = (1 − e)πτ with Eqns (S-4) and (S-6) and then summing up both sides over τ = 090

to ∞, we get:91

f − π0f0 = (1 − e)

(pI + f2n

+n − 1n

∙ f

),

pI − π0pI0 = (1 − e)

1 + f2

.

(S-19)

With Eqn (S-7), we get:92

f0 =1 + e(n − 1)

n(1 + 4e(n − 1)

) ,pI0 =

1 + 2e(n − 1)1 + 4e(n − 1)

,

f =1

1 + 4e(n − 1),

pI =1 + 2e(n − 1)1 + 4e(n − 1)

(= pI

0

),

(S-20)

which recovers Gardner et al.’s (2009) results by replacing ewith 1−(1 − d

)2(where d is female-dispersal93

rate after mating). From this calculation, one may see that the well-known recursions for the94

consanguinity coefficients (Taylor 1988a,b; Frank 1998; Rousset 2004; Lehmann 2007; Gardner et al.95

2009) are evaluated at metapopulation-wide avarage over the patch-age distribution.96

6



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4.2. Haplodiploidy97

Similarly, let us denote the spatially averaged fτ ,ϕτ , μτ over the distribution πτ by f ,ϕ, μ, repsectively:98

f =+∞∑τ=0

πτfτ ,

ϕ =

+∞∑τ=0

πτϕτ ,

μ =+∞∑τ=0

πτμτ ,

pI =

+∞∑τ=0

πτpIτ .

(S-21)

Then the initial values (f0,ϕ0, μ0, pI0) are written as99

f0 =1 + 3f4n

,

ϕ0 =3 + 5f8n

,

μ0 =1 + f2n

,

pI0 =

1 + f2

(S-22)

(because coalescence between offspring born in a patch aged τ = 0 may occur only if they share the100

same mother 1 ∕ n). Also, multiplying πτ = πτ−1 ∙ (1 − e)with the recursions for (fτ ,ϕτ , μτ , pIτ ) (Eqns (S-10)101

to (S-13)) and then summing up both sides over τ = 1, 2,…, supplies:102

+∞∑τ=1

πτfτ =+∞∑τ=1

(1 − e)πτ−1(1 + 3fτ−1

4n+n − 12n

(fτ−1 + ϕτ−1

))

= (1 − e)

(pI + f2n

+n − 12n

(f + ϕ)

) (S-23)

7



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whereas the LHS is f −π0f0 = f −epI + f2n

. Using the similar algebra for (ϕτ , μτ , pIτ ), we get a closed relation103

for (f ,ϕ, μ, pI):104

f − epI + f2n

= (1 − e)pI + f2n

+ (1 − e)n − 12n

(f + ϕ

),

ϕ − e3 + 5f8n

= (1 − e)pI + 2f + 1

4n+ (1 − e)

n − 14n

(ϕ + 2f + μ

),

μ − epI

n= (1 − e)

pI

n+ (1 − e)

n − 1n

ϕ,

pI − e1 + f2

= (1 − e)1 + f2

,

(S-24)

the last line of which implies pI = (1+f ) ∕2,which further implies ϕ =(f + μ

)∕2. With some arrangement,105

we have:106

f =1 + 3f4n

+ (1 − e) ∙n − 1n

∙3f + μ

4,

μ =1 + f2n

+ (1 − e) ∙n − 1n

∙f + μ2

.

(S-25)

In a vector form,107

(f

μ

)=

14n12n

+

34

((1 −

1n

)(1 − e) +

1n

)1 −

1n

4(1 − e)

12

((1 −

1n

)(1 − e) +

1n

)1 −

1n

2(1 − e)

(f

μ

), (S-26)

which gives:108

(f

μ

)=

(1 0

0 1

)−

34

((1 −

1n

)(1 − e) +

1n

)1 −

1n

4(1 − e)

12

((1 −

1n

)(1 − e) +

1n

)1 −

1n

2(1 − e)

−1

14n12n

, (S-27)

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which is solved by:109

f =n

e2n2 − 2e2n + e2 + 3en2 − 2en − e + n,

ϕ =ne − e + 2n

2(e2n2 − 2e2n + e2 + 3en2 − 2en − e + n

) ,μ =

ne − e + ne2n2 − 2e2n + e2 + 3en2 − 2en − e + n

.

(S-28)

Substituting f into the following equations gives the average values of p’s which read:110

pI =1 + f2

,

pS =1 + f2

,

pM = μ

pD =1 + 3f

4,

pF = f .

(S-29)

5 Fitness subcomponents111

Let us focus on a patch aged τ. We denote the mutant sex allocation on the focal patch by xτ , the112

average sex allocation on the same patch by yτ , and the wild type sex allocation on the patch aged τ by113

zτ . In that patch, a focal female produces J(1 − xτ) of females (where J is the number of eggs per capita),114

whomate with the males born on the same patch. If that patch is persistent (with a probability of 1− e),115

female offspring either disperse to recolonize empty patches with a probability of d, or else remain on116

their natal patch with a probability of 1 − d; if they do not disperse, they compete for reproduction117

on the patch against J(1 − d

)(1 − yτ) of non-dispersing females (and therefore the factor J

(1 − d

)is118

cancelled out). If a patch is not persistent (with a probability of e), all females disperse for empty119

patches (e of the whole patches), and such dispersed offspring (J(1 − xτ)((1 − e)d + e

)) compete against120

on average (1 − z)J((

(1 − e)d + e))

of female offspring (and therefore J((1 − e)d + e

)is cancelled out).121

The daughter-fitness of a focal individual inhabiting on the focal patchWFτ is therefore given by:122

WFτ = (1 − e)

(1 − d

)(1 − xτ)(

1 − d)(1 − yτ)

+ e

((1 − e)d + e

)(1 − xτ)(

(1 − e)d + e)(1 − z)

, (S-30)

where we have written the spatial averaged sex allocation for z =∑+∞

j=0 πjzj , and the son-fitness of the123

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focal adult female inhabiting in a patch aged τ,WMτ , is given by:124

WMτ =

xτyτ

((1 − e)

1 − yτ1 − yτ

+ e1 − yτ1 − z

), (S-31)

where we have eliminated the cancelling factors. Note that these fitness functions are defined such125

that neutrality (x = y = z) leads to∑+∞

τ=0 WFτ ≡

∑+∞

τ=0 WMτ ≡ 1.126

Though we presumed in the main text that catastrophic extinction of patches occur after127

reproduction, but Eqns (S-30) and (S-31) can also be hold in other situations; for example: (i) a128

fraction 1 − d of females stays on their natal patch, and a fraction d disperses in the both persistent129

and non-persistent patches, (ii) all females stay on persistent patches, while all females disperse130

on non-persistent patches, and (iii) a fraction 1 − d of females stay and a fraction d disperse on131

persistent patches, while no females survive on non-persistent (extinct) patches. In all cases, the132

dispersal parameter d is cancelled out, and the fitness functions for daughters and sons are simplified133

to Eqns (S-30) and (S-31), respectively.134

We can write the invasion fitness subcomponents in a general form as:135

WFτ = wF(xτ , yτ , z),

WMτ = wM(xτ , yτ , z),

(S-32)

with136

wF(x, y, z) := (1 − e)1 − x1 − y

+ e1 − x1 − z

,

wM(x, y, z) :=xy

((1 − e)

1 − y1 − y

+ e1 − y1 − z

).

(S-33)

It is of use to write down the derivatives:137

∂

∂xwF (x, y, z)

∣∣∣∣∣(x,y,z)=(zτ ,zτ ,z)

= −(1 − e)1

1 − zτ− e

11 − z

∂

∂ywF (x, y, z)

∣∣∣∣∣(x,y,z)=(zτ ,zτ ,z)

= (1 − e)1

1 − zτ,

∂

∂xwM (x, y, z)

∣∣∣∣∣(x,y,z)=(zτ ,zτ ,z)

= (1 − e)1zτ

+ e1 − zτ

zτ(1 − z)

∂

∂ywM (x, y, z)

∣∣∣∣∣(x,y,z)=(zτ ,zτ ,z)

= −(1 − e)1zτ

− e1

1 − z− e

1 − zτzτ(1 − z)

,

(S-34)

where note that the derivatives are evaluated at (x, y, z) = (zτ , zτ , z). These quantities will be used below138

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to assess the direction of selection under weak selection (Taylor & Frank 1996; Frank 1998; Rousset &139

Billiard 2000; Rousset 2004; Taylor et al. 2007).140

6 Total fitness141

Summing up the daughter- and son-mediated fitness functions (per capita) each multiplied by the142

class reproductive values, averaged over the patch-age distribution, obtains the total invasion fitness:143

W =

+∞∑τ=0

(cMτ WM

τ + cFτWFτ

)πτ (S-35)

(Bulmer 1994; Taylor & Frank 1996; Frank 1998; Rousset 2004; Taylor et al. 2007; Lehmann & Rousset144

2010). In particular, if the stratetegy is z = (zE, zN) (with a distribution e : 1 − e),W simplifies to:145

W = e(cMwM (xE, yE, ezE + (1 − e)zN

)+ cFwF (xE, yE, ezE + (1 − e)zN

))+ (1 − e)

(cMwM (xN, yN, ezE + (1 − e)zN

)+ cFwF (xN, yN, ezE + (1 − e)zN

)) (S-36)

where the subscript E accounts for disperser (Emigrant) females (hence inhabiting on the patch aged146

τ = 0), while N accounts for non-disperser females (hence on the patch aged τ > 0). Also we have here147

made it explicit that z = ezE + (1 − e)zN. Also, class reproductive values (Taylor 1990; Caswell 2001) are148

denoted cM for male and cF for females.149

7 Reproductive value150

As the patch-age generates no difference in reproductive capacity, the class reproductive values151

are independent of patch ages and are fully determined by the ploidy: cM = cF = 1 ∕2 for diploidy, and152

cM = 1 ∕3, cF = 2 ∕3 for haplodiploidy (Taylor 1990; Caswell 2001).153

8 Selection gradient154

We outline the analyses for the general case in which the trait to evolve is patch age-specific sex155

ratio sorted as z = (z0, z1,…, zτ ,… ), where zτ represents the sex ratio strategy of a female breeding on a156

patch aged τ. The selection gradients for dispersers’ and non-dispersers’ strategy zE (E for emigrants)157

and zN (N for non-disperser) are, using the neighbor-modulated fitness approach (Taylor & Frank 1996;158

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Frank 1998; Rousset & Billiard 2000; Rousset 2004; Taylor et al. 2007), given by:159

SE(zE, zN) =

(dW0

dg0

)◦

= cM(∂WM

0

∂x0pS0 +

∂WM0

∂y0pM0

)◦

+ cF(∂WF

0

∂x0pD0 +

∂WF0

∂y0pF0

)◦

,

Sτ(zE, zN) =

(dWτ

dgτ

)◦

= cM(∂WM

τ∂xτ

pSτ +

∂WMτ

∂yτpMτ

)◦

+ cF(∂WF

τ∂xτ

pDτ +

∂WFτ

∂yτpFτ

)◦

,

SN(zE, zN) =1

1 − e

+∞∑τ=1

πτSτ(zE, zN),

(S-37)

where ◦ represents neutrality, (i.e., the derivatives are evaluated at x = y = z). gτ represents the genic160

value of a gene sampled from a locus (denoted G, that encodes the sex allocation) of a female offspring161

(Falconer 1975; Grafen 1985; Bulmer 1994; Taylor & Frank 1996; Frank 1998; Gardner et al. 2009). Also,162

p-values are the consanguinities of an adult female with an corresponding offspring sharing the same163

patch (age τ): S designates her own son, M male offspring, D her own daughter, and F female offspring,164

respectively.165

9 Unconditional strategy166

When females exhibit unconditional strategy (i.e., zτ ≡ zU for all τ ≥ 0), the selection gradient reads:167

SU(zU) =+∞∑τ=0

πτSτ(zU, zU). (S-38)

ESS allocation simplifies down to:168

z*U =n − 12n

(S-39)

for diploids, and:169

z*U =cM(pS − pM

)cM(pS − (1 − e)pM

)+ cF

(pD − (1 − e)pF

)=(n − 1)(−1 − e + 3n + en)

2n(−e + 3n + en)

(S-40)

for haplodiploids. We therefore recover Gardner et al.’s (2009) results by replacing e with 1 −(1 − d

)2170

(where d is female-dispersal rate after mating).171

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10 Dispersers’ strategy172

Higher male allocation is favored for a disperser female if:173

cF(−1 − e1 − zE

−e

1 − z

)pD0 +cF

(1 − e1 − zE

)pF0

+cM(1 − ezE

+e(1 − zE)

zE(1 − z)

)pS0 +cM

(−1 − ezE

−e

1 − z−e(1 − zE)

zE(1 − z)

)pM0

> 0. (S-41)

If we divide both sides by pI0 =

(1 + f

)∕ 2 (the consanguinity of a mother to herself), we get the174

Hamilton’s rule of the main text, after clearing the fractions.175

11 Non-dispersers’ strategy176

Higher male allocation is favored for a non-disperser female if:177

+∞∑τ=1

πτ

cF(−1 − e1 − zN

−e

1 − z

)pDτ +cF

(1 − e1 − zN

)pFτ

+cM(1 − ezN

+e(1 − zN)

zN(1 − z)

)pSτ +cM

(−1 − ezN

−e

1 − z−e(1 − zN)

zN(1 − z)

)pMτ

> 0. (S-42)

The quantities inside the bracket are dependent on patch age τ only through consanguinity, p-values.178

Therefore, what matters is the average values of p’s (minus ep0), given that she is in a patch aged τ ≥ 1:179 cF(−1 − e1 − zN

−e

1 − z

)pD − epD

0

1 − e+cF

(1 − e1 − zN

)pF − epF

0

1 − e

+cM(1 − ezN

+e(1 − zN)

zN(1 − z)

)pS − epS

0

1 − e+cM

(−1 − ezN

−e

1 − z−e(1 − zN)

zN(1 − z)

)pM − epM

0

1 − e

> 0. (S-43)

Dividing both sides by∑

τ≥1 pIτπτ ∕ (1 − e) (average consanguinity of a mother to herself in a patch aged180

τ), we get Hamilton’s rule of the main text, after clearing the fractions.181

12 Evolutionary outcomes182

We obtained evolutionary outcomes (z*E , z*N) by nullifying the Hamilton’s rules, and we call the pair183

of the evolutionary outcomes as cESSs (the candidate ESSs; Maynard Smith & Price 1973; Hofbauer &184

Sigmund 1990; Geritz et al. 1998).185

Sensitivity to the number of females ovipositing on a patch, n186

The cESSsmonotonically increase with n, and eventually lead to Fisherian sex ratio 1/2 with n → +∞187

(Supplementary Fig 3- 1A). When we compare z*E and z*N , we found that z*E > z*N always holds true for188

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diploids. The cESSs generally increase with decreasing patch extinction rate e (Supplementary Fig189

3- 1A; but except large n for haplodiploidy), which is likely to be because local competition between190

related females increases with smaller e (Bulmer 1986; Taylor 1988b; Frank 1998; Gardner et al. 2009).191

However, we found the predicted patterns complicated for haplodiploids. For intermediate or high192

extinction rates (for example, e = 0.5 or 0.8), z*E > z*N is also favoured. In contrast, for small e(= 0.2),193

small n favours z*E > z*N while the opposite z*E < z*N appears to occur when n is larger. This trend can be194

explained by relatedness asymmetry for haplodiploid sex determination. For dispersers, inbreeding195

increases relatedness of mothers to their daughters, but does not relatedness to their sons, which196

favours a more female-biased sex ratio for haplodiploid than diploid species (Supplementary Fig197

3- 1A; Frank 1985; Herre 1985). This trend is remarkable with smaller e (i.e., higher inbreeding rates).198

For non-dispersers, mothers are related not only with their own offspring but also with offspring199

produced by other mothers on the same patch. This leads to almost identical cESSs between diploids200

and haplodiploids (Supplementary Fig 3- 1A; Hamilton’s rules for non-dispersers are exactly identical201

for diploids and haplodiploids). Consequently, z*E is predicted to be more female biased than z*N , when202

e is small and n is large.203

Overall, the cESSs are predicted to increase with n, and decrease with inbreeding rates, in agreement204

with to the prediction by a theoretical model assuming that females are able to adjust their offspring205

sex ratio according to the number and kinship of females laying eggs on a patch (Gardner & Hardy206

2020).207

Sensitivity to relatedness between offspring on a patch208

In the present model, the influences of the number of mothers and relatedness between mothers209

on a patch can be summarized to one parameter, relatedness between offspring on a patch. We define210

relatedness between female offspring on a patch produced by dispersers and non-dispersers as:211

RFE :=

f0pI0

(S-44)

and212

RFN :=

11 − e

∑τ≥1 fτπτ

11 − e

∑τ≥1 pI

τπτ=

f − ef0pI − epI

0

(S-45)

respectively. We first assessed the effects of n (the number of mothers ovipositing on a patch) on213

the relatedness coefficients, and found that relatedness coefficients decrease with n and that RFN > RF

E214

(Supplementary Fig 3- 2), which is because non-disperser females are more likely to be related with215

neighboring females than are disperser females (El Mouden & Gardner 2008; Wild & Fernandes 2009).216

By plotting the cESSs against the relatedness (by tuning n), we found that more female-biased sex217

ratios are favoured with increasing relatedness between offspring (Supplementary Fig 3- 1B). This218

negative relationship is predicted for both dispersers and non-dispersers, although the detailed patterns219

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depend on the difference of ploidy. While z*N is similar for diploids and haplodiploids, z*E is more female220

biased for haplodiploid than diploids especially with smaller RFE and smaller e. Consequently, cESSs221

for dispersers and non-dispersers are predicted to switch at an intermediate value of relatedness for222

haplodiploid species (Supplementary Fig 3- 1B).223

By plotting the cESSs in terms of relatedness, we can separately investigate the effects of relatedness224

and local competition between relatives (Cooper et al. 2018). Here, the scale of competition equals225

1 − e, which is the probability that two randomly chosen females laying eggs on a patch are derived226

from the same patch (Frank 1998). We found that less female-biased sex ratios are predicted with227

higher local competition (smaller e) for both dispersers and non-dispersers (Supplementary Fig 3- 1B;228

see also Gardner et al. 2009, in which the scale of competition is(1 − d

)2, where d is female dispersal229

rate). In the natural populations, the effects of relatedness and local competition between relatives are230

likely to influence the evolution of sex ratio, with its extent dependent upon life history details, such231

as population structure and whether females can assess if they are with closer relatives (Frank 1985;232

Frank 1986; Frank 1998; Bulmer 1986; Taylor 1988b; Gardner et al. 2009; Lehmann & Rousset 2010;233

Cooper et al. 2018; Gardner & Hardy 2020).234

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https://doi.org/10.1101/2020.11.16.384768


(A)Diploid, e = 0.2

2 4 6 8 10 12 14 160.0

0.1

0.2

0.3

0.4

0.5

0.6

Number of mothers (n)

Sexratio zE

zU

zN

Diploid, e = 0.5

2 4 6 8 10 12 14 160.0

0.1

0.2

0.3

0.4

0.5

0.6


Sexratio zE

zU

zN

Diploid, e = 0.8

2 4 6 8 10 12 14 160.0

0.1

0.2

0.3

0.4

0.5

0.6


Sexratio zE

zU

zN

Haplodiploid, e = 0.2

2 4 6 8 10 12 14 160.0

0.1

0.2

0.3

0.4

0.5

0.6


Sexratio zE

zU

zN


2 4 6 8 10 12 14 160.0

0.1

0.2

0.3

0.4

0.5

0.6


Sexratio zE

zU

zN


2 4 6 8 10 12 14 160.0

0.1

0.2

0.3

0.4

0.5

0.6


Sexratio zE

zU

zN

(B)Diploid, e = 0.2

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

Relatedness

Sexratio

zE

zN

Diploid, e = 0.5

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

Relatedness

Sexratio

zE

zN

Diploid, e = 0.8

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

Relatedness

Sexratio

zE

zN


0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

Relatedness

Sexratio

zE

zN


0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

Relatedness

Sexratio

zE

zN


0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

Relatedness

Sexratio

zE

zN

Supplementary Fig 3- 1: Predicted sex ratio (proportion sons) plotted against the number of femalesovipositing on a patch (n; panel A) and against the relatedness coefficient for female offspring on apatch RF

E for dispersers and RFN for non-dispersers (panel B).

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Diploid, e = 0.2

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0


Relatedn

ess

RNF

REF

Diploid, e = 0.5

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0


Relatedn

ess

RNF

REF

Diploid, e = 0.8

0 5 10 150.0

0.2

0.4

0.6

0.8

1.0

Number of mothers (n)Re

latedn

ess

RNF

REF


0 5 10 150.0

0.2

0.4

0.6

0.8

1.0


Relatedn

ess

RNF

REF


0 5 10 150.0

0.2

0.4

0.6

0.8

1.0


Relatedn

ess

RNF

REF


0 5 10 150.0

0.2

0.4

0.6

0.8

1.0


Relatedn

ess

RNF

REF

Supplementary Fig 3- 2: Relatedness coefficients plotted against n.

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https://doi.org/10.1101/2020.11.16.384768


solving the sex ratio scandal in melittobia wasps · 2020. 11. 16. · produce less female-biased...

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